The operator \(F_{k(1)}\)  is a sum over the intermediate colors labeling each 4-valent bubbles: \(F_{k(1)}=\sum _{i=1}^5F_{k(1)}^{(i)}\) , and each term contribute separately to the wave function and mass flow. As a result, we focus our attention on the computation of the trace for the case \(i=1\) . As explained in [1]}, we will identify the contribution to the coupling of a given bubble in the l.h.s by expanding the r.h.s around its local approximation i.e. around the value \(q=0\) , where \(q\)  denote the "external momentum" shared by the red lines in the Figure (REF ). The two-points case is in a sense the more interesting, because for the wave function contribution, the local expansion require the first deviation to the exact local approximation, corresponding to the mass-term. This first deviation is proportional to \(q^2\) . Then, identifying the terms in front of each powers of \(q^2\) , we find:
\(k\partial _km^2(k)=-5\lambda _1(k)\frac{k\partial _kZ(k)(S_1(0)k^2-S_2(0))+2Z(k)k^2S_1(0)}{[Z(k)k^2+m^2(k)]^2}\) 
